PBZ*-Lattices: Structure Theory and Subvarieties-Reference-Cited by-同舟云学术

PBZ*-Lattices: Structure Theory and Subvarieties

Published:2020 Issue: Volume:55 Page:3-39
ISSN:2084-2589
Container-title:Reports on Mathematical Logic
language:en
Short-container-title:

Author:

Giuntini Roberto¹,Mureşan Claudia²,Paoli Francesco¹

Affiliation:

1. Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy

2. Faculty of Mathematics and Computer Science, University of Bucharest, Romania

Abstract

We investigate the structure theory of the variety of PBZ*-lattices and some of its proper subvarieties. These lattices with additional structure originate in the foundations of quantum mechanics and can be viewed as a common generalisation of orthomodular lattices and Kleene algebras expanded by an extra unary operation. We lay down the basics of the theories of ideals and of central elements in PBZ*-lattices, we prove some structure theorems, and we explore some connections with the theories of subtractive and binary discriminator varieties.

Publisher

Uniwersytet Jagiellonski - Wydawnictwo Uniwersytetu Jagiellonskiego

Subject

Logic,Philosophy

Reference26 articles.

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5. 5. G. Bruns, J. Harding, Algebraic aspects of orthomodular lattices, In: Current Research in Operational Quantum Logic (Eds. B. Coecke et al.), Springer, Berlin, 2000, pp. 37-65.

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